> Because something can't be represented exactly, it > doesn't or can't exist? For this fellow, knowledge of pi to beyond what is > sufficient accuracy to send landers to Mars is insufficient to conclude it > exists and is natural! Talk about silly!
Bob, The concept or principle exists. The number to describe it is what doesn't. Pi exists in nature not as a number or a name. Both of those are symbols of a descriptor, accurate so far as we know. A great many of the descriptive symbols and words that we have used throughout history have been proven now to have no validity. A lot of it even still exists in our spoken language. "Music of the spheres"? Well, the "shperes" in the astronomical sense no longer exist. Virtually all the cosmography in, say, Milton's _Paradise Lost_ is fantasy. Is "Dragon" real? Is "Zeus" a real thing in nature? To certain cultures they were once real. According to our culture and the present state of knowledge, the symbols don't adequately describe reality. The number "pi" may hold up as an accurate description of what it describes. But there is nothing about _the way we define it_ that dictates to nature what nature must be. It's not _causal_. Just as likely, mathematicians of the future will devise a better, more elegant way of describing and understanding what we know as pi. Their history books will read that we used a crude irrational number as a way of understanding what was really going on...doing the best we could. You could find good ways into this argument through a number of disciplines, interestingly enough. Number theory is one; quantum mechanics is another that would do; even reading Noam Chomsky. Also, studies in neurology (ever read Oliver Sachs' famous book _The Man Who Mistook His Wife For a Hat_?). All these can give insight into how our brains relate to concepts through symbols in the context of cultural conditioning. There are no numbers in nature, except, possibly, one--er, one. That is, "one" may be a number that actually does exist in nature. Does it? We're not sure. Nobody's proved it yet, but nobody's disproved it. That's the whole question of entity in number theory. And number theory is a mess right now. <g> --Mike
